Another related quantity exploits directly the luminosity of the system either in the optical (B) or infrared (K) bands: it is the ratio of the iron mass to the total light of the cluster/group [1]}, [2]}. If different metals in addition to iron are measured then the specific element MLR can be estimated, like for example O and Si MLRs.
These quantities are even more important to consider given the trends of stellar and gas fractions (and their sum, the baryon fraction) as a function of total mass which clearly mark the scale of groups as a crucial one in comparison with clusters. The derived baryon fraction for rich clusters is consistent with the cosmic baryon fraction, \(\Omega _b/\Omega _M \sim 0.15\)  [3]} as obtained with X-ray, optical and infra-red observations [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}
On the other hand, groups are characterized by higher stellar mass and lower IGrM mass fractions than rich clusters, and the number of baryon fraction tends to be lower with smaller groups [11]}, [12]}, [13]}, [14]}.
Explanations of this discrepancy are suggested in the above references as follows: 1. different physical processes depending on the system mass, like for example a different efficiency of baryon-to-stars conversion; 2. observational data missing for fainter sources (as for example the intra-cluster light component) and for the IGRM at large radii; 3. systematic errors for the mass estimations; 4. non-gravitational heating and metal mixing by AGN feed back [15]}, [16]}, but a definitive solution has not been reached yet. As for the non-gravitational effect such as AGN feedback, the entropy profiles are good probe to estimate for each group and cluster, and we describe it in the following paragraph.
